In the first part of the talk, we examine fundamental limitations
arising from the use of local feedback in networks subject to
stochastic disturbances. For vehicular formation control problems in
topology of regular lattices we show that it is impossible to have
coherent large formations, that behave like rigid lattices, in one and
two spatial dimensions. Yet we prove that this is achievable in 3D.
The observed phenomenon is a consequence of the fact that, in 1D and
2D, local feedback laws are ineffective in guarding against
disturbances with large spatial wavelength. We provide connections
with several other problems including distributed averaging
algorithms, global mean first passage time of random walks, effective
resistance in electrical networks, and statistical mechanics of
harmonic solids.

In the second part of the talk, we demonstrate how tools and ideas
from control theory, optimization, and compressive sensing can be
combined to identify network topologies that strike desired tradeoff
between the performance and sparsity. Our approach consists of two
steps. First, we identify sparsity patterns of the feedback gains by
incorporating sparsity-promoting penalty functions into the optimal
control problem, where the added terms penalize the number of
communication links in the distributed controller. Second, we optimize
feedback gains subject to structural constraints determined by the
identified sparsity patterns. In the first step, the sparsity
structure of feedback gains is identified using the alternating
direction method of multipliers, an algorithm well-suited to large
optimization problems. Several examples are provided to demonstrate
the effectiveness of the developed approach.

Bio sketch:

Mihailo Jovanovic (www.umn.edu/~mihailo) is an Associate Professor of
Electrical and Computer Engineering at the University of Minnesota,
Minneapolis, where he also serves as the Director of Graduate Studies
in the interdisciplinary PhD program in Control Science and Dynamical
Systems. He has held visiting positions with Stanford University and
the Institute for Mathematics and its Applications. His current
research focuses on sparsity-promoting optimal control, fundamental
performance limitations in the design of large dynamic networks, and
dynamics and control of fluid flows. He is a senior member of IEEE,
and a member of APS and SIAM. He currently serves as an Associate
Editor of the SIAM Journal on Control and Optimization and has served
as an Associate Editor of the IEEE Control Systems Society Conference
Editorial Board from July 2006 until December 2010. He received a
CAREER Award from the National Science Foundation in 2007, an Early
Career Award from the University of Minnesota Initiative for Renewable
Energy and the Environment in 2010, a Resident Fellowship within the
Institute on the Environment at the University of Minnesota in 2012,
and the George S. Axelby Outstanding Paper Award from the IEEE Control
Systems Society in 2013.